Mathematics

Problem

(Long Answer – Procedural Application) Consider the function

f(x)=|x-3|+2, \quad x\in\mathbb R.

(a) Locate all critical points of

f

. (b) Determine the sign of

f'(x)

for

x<3

and

x>3

. (c) Using your answer to part (b), state whether

f

has a local maximum, a local minimum or neither at each critical point. (d) Write the intervals on which

f

is increasing and those on which it is decreasing.